If I recall correctly.......that only came about after the 3rd world war, and rise of the Supermen , like Kahn, who were ultimately defeated and then shot into space, in a cryogenic state only to be found floating adrift, many centuries later by Kirk and the Enterprise.
Even in the Next Generation timeline, when they go back in time, to invent Warp Drive......
they go back to an earth that has been largely destroyed, and people are living in the wilds, like survivors of a post apocolyptic earth.
It is that experiment...where they achieve only .5 Warp drive that draws the attention of the Vulcans, who just so happened to be passing by, and picked up the warp drive signature. That's how Vulcans finally came to Earth for the first time.